Parameter selection in permutation entropy for an electroencephalographic measure of isoflurane anesthetic drug effect

The permutation entropy (PE) of the electroencephalographic (EEG) signals has been proposed as a robust measure of anesthetic drug effect. The calculation of PE involves the somewhat arbitrary selection of embedding dimension (m) and lag (τ) parameters. Previous studies of PE include the analysis of EEG signals under sevoflurane or propofol anesthesia, where different parameter settings were determined using a number of different criteria. In this study we choose parameter values based on the quantitative performance, to quantify the effect of a wide range of concentrations of isoflurane on the EEG. We analyzed a set of previously published EEG data, obtained from 29 patients who underwent elective abdominal surgery under isoflurane general anesthesia combined with epidural anesthesia. PE indices using a range of different parameter settings (m = 3–7, τ = 1–5) were calculated. These indices were evaluated as regards: the correlation coefficient (r) with isoflurane end-tidal concentration, the relationship with isoflurane effect-site concentration assessed by the coefficient of determination (R2) of the pharmacokinetic–pharmacodynamic models, and the prediction probability (PK). The embedding dimension (m) and lag (τ) have significant effect on the r values (Two-way repeated-measures ANOVA, p < 0.001). The proposed new permutation entropy index (NPEI) [a combination of PE(m = 3, τ = 2) and PE(m = 3, τ = 3)] performed best among all the parameter combinations, with r = 0.89(0.83–0.94), R2 = 0.82(0.76–0.87), and PK = 0.80 (0.76–0.85). Further comparison with previously suggested PE measures, as well as other unrelated EEG measures, indicates the superiority of the NPEI. The PE can be utilized to indicate the dynamical changes of EEG signals under isoflurane anesthesia. In this study, the NPEI measure that combines the PE with m = 3, τ = 2 and that with m = 3, τ = 3 is optimal.